Stochastic control applications and higher-order approximation of strongly coupled Forward-Backward Stochastic Differential Equations

点击翻译按钮获取中文摘要

The project deals with Forward-Backward Stochastic Differential Equations (FBSDEs). In the first part of the project we will analyze a particular class of stochastic control problem, referred to as target problem, that consists in minimizing a cost functional over a class of absolutely continuous paths vanishing at a given terminal time. By applying the stochastic maximum principle one can reduce the problem to a FBSDE. The project's first main aim is to understand to which extent one can solve the associated FBSDEs, and hence the original target problems. We plan to advance a new method, called method of decoupling fields, for showing whether a strongly coupled FBSDEs possesses a solution or not. We will hereby strive to keep the objective functional of the stochastic control problem as general as possible.The project's second objective is to develop algorithms that allow to compute higher-order approximations of strongly coupled FBSDEs. To this end we will draw on Ito-Taylor-expansions of the systems. We will set up an algorithm estimating the coefficients of the Ito-Taylor-expansion implicitly by minimizing a suitable error functional. The goal is to prove the convergence properties of such enhanced algorithms.